We are looking at a new truck. The ad states "GVWR 9,900 lbs." This is an F250, 2015 model, with a 6.7 liter engine. What does the GVWR mean? Is it how much the truck can weigh with a load of stuff in it?

Yes, it is the manufacturer's rating for the max. weight of the truck. However, there is a lot more involved. In many states (don't know about provinces) you can register the truck up to the total of the front and rear GAWRs. Or you can register it for less than the GVWR, but you better keep it under that registered number.

Also, I assume you understand that generally, the F250 and F350 are the same truck mechanically except for rear springs, tires and wheels. And the F250 can be optioned with those same components and have the same rear GAWR as the F350, but still have just a 9900 lb GVWR. So an F250 with the right options is just as capable as the F350, but lacks the higher GVWR. If your state (or province) allows higher registration, you can register a properly equipped F250 for the same loaded weight as the F350.

GVWR: gross vehicle weight rating. This is the most your truck can weigh with everything in or on it (this will include pets, people, gear, hitch and tongue/pin weight)
GCWR : gross combined weight rating. This is the truck GVWR plus trailer GVWR.

Available payload: gvwr - truck actual weight (occupants plus yongue/pin weight should be less than this)

Adjusted towing capacity: GCWR - actual truck weight

When shopping for a truck check the tire loading sticker inside the drivers side door for "occupants and cargo should weigh less than x lbs"

Honestly getting the 350/3500 truck with the higher GVWR will gain you much more payload and towing capacity to handle pin weight/trailer weight.

Forgot to add, a friend has an F250 optioned as I described, the camper package I believe provides the F350 leaf springs and optional tires/wheels are the stock F350 ones. So, his rear GAWR is 7000 lbs, tires have a 7500 lb load capacity (at 80 psi). However, his door sticker shows the 9900 lb GVWR since it is just an F250. But what is worse, the sticker also shows max. tire inflation of just 65 psi (assuming stock F250 tires). So he was maintaining tire pressure between 60-65 psi while towing a 38 ft Life Style fiver with a dry pin weight of 2800 lbs. At 65 psi he was seriously overloading the tires, but if he had just inflated them based on the sidewall rather than the door sticker he would have been OK technically (and legally if the selling dealer had registered the truck properly).